An introduction to the mathematical formulation of self-organizing systems : John Formby. 200 pages, diagrams, 6 × 9 in. London, England, E. and F.N. Spon, Ltd.
✍ Scribed by Thomas J. Higgins
- Publisher
- Elsevier Science
- Year
- 1969
- Tongue
- English
- Weight
- 192 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0016-0032
No coin nor oath required. For personal study only.
✦ Synopsis
Book Reviews
found, and the reader who wishes to fully understand them will need to do some work. It could well be said that this article alone is worth the price of the book if that price were not so outrageous, even for a book of 241 pages, let alone an article of 69 pages.
Sagdeev begins with a general discussion of cooperative phenomena in a plasma characterized by a far higher ratio of cogency to hand-waving than usually informs articles on this subject. He then discusses the topic of non-linear oscillations, of various kinds. Here his principal thesis is that whereas shock structure and similar phenomena in gas dynamics are determined by the competition between steepening of wave fronts (due to the tendency of waves of higher velocity to overtake slower waves) and dissipative effects, in a collisionless plasma the role of the latter is taken over by dispersive effects: when the relation between frequency and wave-number becomes non-linear, energy transfer to harmonics of the fundamental becomes inefficient, thus suppressing non-linear distortions of the wave. He illustrates this with several concrete examples, with and also without an external magnetic field, and then proceeds to apply the notions he has developed to the question of shock structure. This is confined mostly to the case where the flow behind the shock is laminar, consisting of large amplitude oscillations. While he shows that this treatment cannot apply when the amplitudes become too large, he does not treat in detail the turbulent flow which presumably results. Much of the material in this article is based upon previous publications by Sagdeev and his collaborators, references to which are given. In summary, the articles by Volkov and Sivukhin are competent, but not distinguished, reviews, quite suitable for graduate students new to the field. The one by Sagdeev should be instructive to plasma theorists interested in cooperative phenomena, including the experts.